Brain Connectivity Networks in Theory and Practice

Abstract

The main purpose of this thesis is to develop statistical methods to explore the human brain connectivity and its relationship to cognitive diseases, such as Alzheimer's disease. Among a variety of different imaging methods, resting-state functional magnetic resonance imaging (rs-fMRI) data are popularly used for estimating brain connectivity networks in the absence of tasks. In neuroimaging, Gaussian graphical models are mainstream tools for modeling statistical dependencies as functional connectivity across anatomically distinct regions of the human brain. Brain connectivity here is an undirected graph estimated from high-dimensional fMRI data. We show, however, that standard Gaussian graphical modeling methods such as neighborhood selection and graphical lasso can fail to provide accurate and reproducible graph recovery when estimating brain connectivity networks. This problem persists even under the best circumstances of optimal tuning and sufficiently large sample sizes, which is often not achieved in real applications with these methods. In Chapter 1, we attempt to solve this problem by leveraging the three-dimensional spatial positions of the nodes into a neighborhood selection framework to gain more accurate graph estimations. These positions are incorporated into the tuning parameters of each nodes' penalized regression in the form of pairwise distances between brain regions. This approach (named SI) is motivated by the biological rationale that direct brain connections are more likely between close regions than between distant regions. Clinically, fMRI data is often obtained longitudinally for each subject. However, discussion for estimating networks in a longitudinal clinical setting are scarce. Human brain connectivity has been shown to be reproducible across individuals. Recent advances in data acquisition and preprocessing have also largely improved the reliability of functional magnetic resonance imaging for estimating functional brain networks. In Chapter 3, driven by these developments, we exploit the presence of shared connectivity structure in order to produce more accurate brain connectivity estimates for individual patients in clinical settings. More specifically, we propose an approach that can incorporate information from baseline fMRI assessment when estimating networks in follow-up fMRI data. For this new approach (named Geofuse), we manage to jointly estimate two graphs under one neighborhood selection model. For each regression, we add an additional fused lasso penalty on the basis of Geofuse from Chapter 1 to encourage the two groups of parameters for the two graphs to shrink together, yielding more stable networks across repeated scans of the same individuals. Both approaches SI and Geofuse are computationally convenient and efficient. Using data from an Alzheimer's disease dataset and the Consortium for Reliability and Reproducibility, we illustrate that SI (for single graph estimation) and Geofuse (for joint graph estimation) both produce more stable brain connectivity networks than state of the art methods. These two approaches may, therefore, be of particular value to the clinical neurosciences. In Chapter 2, we study a topic outside of neuroscience, namely personalized medicine. Sometimes, the development of a market-ready companion diagnostic test (CDx) for identifying the best treatment for individual patients may lag behind the development of the actual drug, and we use a clinical trial assay (CTA) to enroll patients into the drug pivotal clinical trial instead. Thus, when CDx becomes available, a bridging study is required to assess the drug efficacy in the CDx intended use population (CDx IU). Due to randomization related missingness of the CDx results, one challenge we face is covariate imbalance between treatment arms for the subpopulation with both positive CDx and CTA. In Chapter 2, we address this challenge in bridging studies under a causal inference framework and evaluate the performance of two methods: 1) the propensity score method with doubly robust estimation. 2) the optimal matching method.